Analysis of a post-fracture pressure buildup test with wellbore-storage distortion

Input(s)

\(q_{g}\): Gas flow rate (MSCF/day)

\(B_{g}\): Gas formation Volume Factor (RB/MSCF)

\(p_{D}\): Dimensionless Pressure (dimensionless)

\(\varnothing\): Porosity (dimensionless)

\(c_{t}\): Compressibility \((1 / \mathrm{psi})\)

\(\mu\): Viscosity \((\mathrm{cP})\)

\(\mathrm{h}\): Formation Thickness (ft)

\(t_{\left(L_{\rangle_{D}}\right.}\): Time of end of linear or pseudo radial flow from plot (dimensionless)

\(C_{r D}\): Dimensionless fracture conductivity (dimensionless)

\(C_{f D}\): Dimensionless Wellbore storage coefficient (dimensionless)

\(L_{f}\): Length of fracture \((\mathrm{ft})\)

\(\mathrm{k}\): Permeability \((\mathrm{mD})\)

\(\Delta t_{A E}\): Equivalent Adjusted delta time from derivative curve (h)

Output(s)

C: Well bore storage coefficient (bbl/psi)

\(w_{f k_{f}}\): Min Fracture conductivity for infinite conductive fracture \((\mathrm{mD} \mathrm{ft})\)

\(L_{f M P}\): Length of fracture from match point analysis (ft)

\(\left(\Delta P_{a}\right)_{M P}\): Adjusted Pressure difference at match point from plot (psi)

Formula(s)

Reference(s)

Lee, J., Rollins J.B., and Spivey J.P. 2003, Pressure Transient Testing, Vol. 9, SPE Textbook Series, Vol. 9 , Henry L. Doherty Memorial Fund of AIME, Richardson, Texas, SPE, Chapter: 6, Page: 127.